Yes. Usually the summer after junior year, although a lot of applicants are now doing IB internships in the summer after their sophomore year as well (usually a boutique but some BBs have sophomore programs now).

Something cool/unique the summer after Freshman year --> Finance/IB internship the summer after Sophomore Year --> Main IB Internship the summer after Junior Year (where you can hopefully get a return offer for full-time) --> Start Full-Time the summer after you graduate Senior year

Sure, anything is cool - it just depends on how you spin-it. If you're really into sports and did a marketing internship for the NFL, that's something really awesome. I did a finance internship but abroad in a random country the summer after my Freshman year, and in interviews I always got asked about it. Just have an answer as to why you did it/how it ties into your broader interests or skills you're trying to build out for yourself.